Question

lesson 3 - 4 hw
2.) triangle abc is dilated by a scale factor of 3. the image is triangle abc
side length ab = 10 mm m∠abc = 21°
answer the following
side length ab = ____ m∠abc = ____
3.) quadrilateral abce is dilated to get quadrilateral abce using center f.
what is the scale factor of dilation? show your calculations
4.) triangle a is a dilation of triangle a.
a.) set up proportions and determine the value of the missing side. show work.
b.) what is the scale factor? show your calculations.

Explanation:

Step1: Set up proportion

Let the missing side be \(x\). Since the triangles are similar (due to dilation), we can set up the proportion \(\frac{3}{12}=\frac{x}{16}\).

Step2: Solve the proportion

Cross - multiply: \(12x = 3\times16\). Then \(12x=48\), and \(x = \frac{48}{12}=4\).

Step3: Find the scale factor

The scale factor \(k\) is the ratio of corresponding sides. Using the sides \(3\) and \(12\) (or \(6\) and \(24\)), \(k=\frac{12}{3}=\frac{24}{6} = 4\).

Answer:

a) The missing side is \(4\).
b) The scale factor is \(4\).